Search for steady states of piecewise-linear differential equation models of genetic regulatory networks

Analysis of the attractors of a genetic regulatory network gives a good indication of the possible functional modes of the system. In this paper we are concerned with the problem of finding all steady states of genetic regulatory networks described by piecewise-linear differential equation (PLDE) models. We show that the problem is NP-hard and translate it into a propositional satisfiability (SAT) problem. This allows the use of existing, efficient SAT solvers and has enabled the development of a steady state search module of the computer tool Genetic Network Analyzer (GNA). The practical use of this module is demonstrated by means of the analysis of a number of relatively small bacterial regulatory networks as well as randomly generated networks of several hundreds of genes.     

Qualitatively modelling and analysing genetic regulatory networks: a Petri net approach

MOTIVATION: New developments in post-genomic technology now provide researchers with the data necessary to study regulatory processes in a holistic fashion at multiple levels of biological organization. One of the major challenges for the biologist is to integrate and interpret these vast data resources to gain a greater understanding of the structure and function of the molecular processes that mediate adaptive and cell cycle driven changes in gene expression. In order to achieve this biologists require new tools and techniques to allow pathway related data to be modelled and analysed as network structures, providing valuable insights which can then be validated and investigated in the laboratory. RESULTS: We propose a new technique for constructing and analysing qualitative models of genetic regulatory networks based on the Petri net formalism. We take as our starting point the Boolean network approach of treating genes as binary switches and develop a new Petri net model which uses logic minimization to automate the construction of compact qualitative models. Our approach addresses the shortcomings of Boolean networks by providing access to the wide range of existing Petri net analysis techniques and by using non-determinism to cope with incomplete and inconsistent data. The ideas we present are illustrated by a case study in which the genetic regulatory network controlling sporulation in the bacterium Bacillus subtilis is modelled and analysed. AVAILABILITY: The Petri net model construction tool and the data files for the B. subtilis sporulation case study are available at http://bioinf.ncl.ac.uk/gnapn.     

Inference of biological pathway from gene expression profiles by time delay boolean networks

One great challenge of genomic research is to efficiently and accurately identify complex gene regulatory networks. The development of high-throughput technologies provides numerous experimental data such as DNA sequences, protein sequence, and RNA expression profiles makes it possible to study interactions and regulations among genes or other substance in an organism. However, it is crucial to make inference of genetic regulatory networks from gene expression profiles and protein interaction data for systems biology. This study will develop a new approach to reconstruct time delay Boolean networks as a tool for exploring biological pathways. In the inference strategy, we will compare all pairs of input genes in those basic relationships by their corresponding [Formula: see text]-scores for every output gene. Then, we will combine those consistent relationships to reveal the most probable relationship and reconstruct the genetic network. Specifically, we will prove that [Formula: see text] state transition pairs are sufficient and necessary to reconstruct the time delay Boolean network of [Formula: see text] nodes with high accuracy if the number of input genes to each gene is bounded. We also have implemented this method on simulated and empirical yeast gene expression data sets. The test results show that this proposed method is extensible for realistic networks.     

Perturbation analysis analyzed—mathematical modeling of intact and perturbed gene regulatory circuits for animal development

Gene regulatory networks for animal development are the underlying mechanisms controlling cell fate specification and differentiation. The architecture of gene regulatory circuits determines their information processing properties and their developmental function. It is a major task to derive realistic network models from exceedingly advanced high throughput experimental data. Here we use mathematical modeling to study the dynamics of gene regulatory circuits to advance the ability to infer regulatory connections and logic function from experimental data. This study is guided by experimental methodologies that are commonly used to study gene regulatory networks that control cell fate specification. We study the effect of a perturbation of an input on the level of its downstream genes and compare between the cis-regulatory execution of OR and AND logics. Circuits that initiate gene activation and circuits that lock on the expression of genes are analyzed. The model improves our ability to analyze experimental data and construct from it the network topology. The model also illuminates information processing properties of gene regulatory circuits for animal development.     

Gradient Descent Optimization in Gene Regulatory Pathways

Background

Gene Regulatory Networks (GRNs) have become a major focus of interest in recent years. Elucidating the architecture and dynamics of large scale gene regulatory networks is an important goal in systems biology. The knowledge of the gene regulatory networks further gives insights about gene regulatory pathways. This information leads to many potential applications in medicine and molecular biology, examples of which are identification of metabolic pathways, complex genetic diseases, drug discovery and toxicology analysis. High-throughput technologies allow studying various aspects of gene regulatory networks on a genome-wide scale and we will discuss recent advances as well as limitations and future challenges for gene network modeling. Novel approaches are needed to both infer the causal genes and generate hypothesis on the underlying regulatory mechanisms.

Methodology

In the present article, we introduce a new method for identifying a set of optimal gene regulatory pathways by using structural equations as a tool for modeling gene regulatory networks. The method, first of all, generates data on reaction flows in a pathway. A set of constraints is formulated incorporating weighting coefficients. Finally the gene regulatory pathways are obtained through optimization of an objective function with respect to these weighting coefficients. The effectiveness of the present method is successfully tested on ten gene regulatory networks existing in the literature. A comparative study with the existing extreme pathway analysis also forms a part of this investigation. The results compare favorably with earlier experimental results. The validated pathways point to a combination of previously documented and novel findings.

Conclusions

We show that our method can correctly identify the causal genes and effectively output experimentally verified pathways. The present method has been successful in deriving the optimal regulatory pathways for all the regulatory networks considered. The biological significance and applicability of the optimal pathways has also been discussed. Finally the usefulness of the present method on genetic engineering is depicted with an example.     

Modeling and simulation of genetic regulatory systems: a literature review.

In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.     

Sparse graphical Gaussian modeling of the isoprenoid gene network in Arabidopsis thaliana

We present a novel graphical Gaussian modeling approach for reverse engineering of genetic regulatory networks with many genes and few observations. When applying our approach to infer a gene network for isoprenoid biosynthesis in Arabidopsis thaliana, we detect modules of closely connected genes and candidate genes for possible cross-talk between the isoprenoid pathways. Genes of downstream pathways also fit well into the network. We evaluate our approach in a simulation study and using the yeast galactose network.     

Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks

MOTIVATION: Bayesian networks have been applied to infer genetic regulatory interactions from microarray gene expression data. This inference problem is particularly hard in that interactions between hundreds of genes have to be learned from very small data sets, typically containing only a few dozen time points during a cell cycle. Most previous studies have assessed the inference results on real gene expression data by comparing predicted genetic regulatory interactions with those known from the biological literature. This approach is controversial due to the absence of known gold standards, which renders the estimation of the sensitivity and specificity, that is, the true and (complementary) false detection rate, unreliable and difficult. The objective of the present study is to test the viability of the Bayesian network paradigm in a realistic simulation study. First, gene expression data are simulated from a realistic biological network involving DNAs, mRNAs, inactive protein monomers and active protein dimers. Then, interaction networks are inferred from these data in a reverse engineering approach, using Bayesian networks and Bayesian learning with Markov chain Monte Carlo. RESULTS: The simulation results are presented as receiver operator characteristics curves. This allows estimating the proportion of spurious gene interactions incurred for a specified target proportion of recovered true interactions. The findings demonstrate how the network inference performance varies with the training set size, the degree of inadequacy of prior assumptions, the experimental sampling strategy and the inclusion of further, sequence-based information. AVAILABILITY: The programs and data used in the present study are available from http://www.bioss.sari.ac.uk/~dirk/Supplements     

VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development

Plant organs, including leaves and roots, develop by means of a multilevel cross talk between gene regulation, patterned cell division and cell expansion, and tissue mechanics. The multilevel regulatory mechanisms complicate classic molecular genetics or functional genomics approaches to biological development, because these methodologies implicitly assume a direct relation between genes and traits at the level of the whole plant or organ. Instead, understanding gene function requires insight into the roles of gene products in regulatory networks, the conditions of gene expression, etc. This interplay is impossible to understand intuitively. Mathematical and computer modeling allows researchers to design new hypotheses and produce experimentally testable insights. However, the required mathematics and programming experience makes modeling poorly accessible to experimental biologists. Problem-solving environments provide biologically intuitive in silico objects ("cells", "regulation networks") required for setting up a simulation and present those to the user in terms of familiar, biological terminology. Here, we introduce the cell-based computer modeling framework VirtualLeaf for plant tissue morphogenesis. The current version defines a set of biologically intuitive C++ objects, including cells, cell walls, and diffusing and reacting chemicals, that provide useful abstractions for building biological simulations of developmental processes. We present a step-by-step introduction to building models with VirtualLeaf, providing basic example models of leaf venation and meristem development. VirtualLeaf-based models provide a means for plant researchers to analyze the function of developmental genes in the context of the biophysics of growth and patterning. VirtualLeaf is an ongoing open-source software project (http://virtualleaf.googlecode.com) that runs on Windows, Mac, and Linux.     

Using a State-Space Model and Location Analysis to Infer Time-Delayed Regulatory Networks

Computational gene regulation models provide a means for scientists to draw biological inferences from time-course gene expression data. Based on the state-space approach, we developed a new modeling tool for inferring gene regulatory networks, called time-delayed Gene Regulatory Networks (tdGRNs). tdGRN takes time-delayed regulatory relationships into consideration when developing the model. In addition, a priori biological knowledge from genome-wide location analysis is incorporated into the structure of the gene regulatory network. tdGRN is evaluated on both an artificial dataset and a published gene expression data set. It not only determines regulatory relationships that are known to exist but also uncovers potential new ones. The results indicate that the proposed tool is effective in inferring gene regulatory relationships with time delay. tdGRN is complementary to existing methods for inferring gene regulatory networks. The novel part of the proposed tool is that it is able to infer time-delayed regulatory relationships.     

Probabilistic representation of gene regulatory networks

MOTIVATION: Recent experiments have established unambiguously that biological systems can have significant cell-to-cell variations in gene expression levels even in isogenic populations. Computational approaches to studying gene expression in cellular systems should capture such biological variations for a more realistic representation. RESULTS: In this paper, we present a new fully probabilistic approach to the modeling of gene regulatory networks that allows for fluctuations in the gene expression levels. The new algorithm uses a very simple representation for the genes, and accounts for the repression or induction of the genes and for the biological variations among isogenic populations simultaneously. Because of its simplicity, introduced algorithm is a very promising approach to model large-scale gene regulatory networks. We have tested the new algorithm on the synthetic gene network library bioengineered recently. The good agreement between the computed and the experimental results for this library of networks, and additional tests, demonstrate that the new algorithm is robust and very successful in explaining the experimental data. AVAILABILITY: The simulation software is available upon request. SUPPLEMENTARY INFORMATION: Supplementary material will be made available on the OUP server.     

Population and quantitative genetics of regulatory networks

I evolved boolean regulatory networks in a computer simulation. I varied mutation, recombination, the size of the network, and the number of connections per node. I measured the performance of networks and the heritability and epistasis of genetic effects. Networks of intermediate connectivity performed best. The distinction between metabolic and quantitative genetic additivity explained some of the variation in performance. Metabolic additivity describes the interaction between changes in a single network, whereas quantitative genetic additivity measures the consistency of phenotypic effect caused by gene substitution in randomly chosen members of the population. I analysed metabolic additivity by the distribution of epistatic effects of pairs of mutations in individual networks. I measured quantitative genetic additivity by heritability. Highly connected networks had greater metabolic additivity for perturbations to individual networks, but had lower additivity when measured by the average effect of a gene substitution (heritability). The lower heritability of highly connected nets appeared to reduce the effectiveness of recombination in searching evolutionary space.     

Structural systems identification of genetic regulatory networks

MOTIVATION: Reverse engineering of genetic regulatory networks from experimental data is the first step toward the modeling of genetic networks. Linear state-space models, also known as linear dynamical models, have been applied to model genetic networks from gene expression time series data, but existing works have not taken into account available structural information. Without structural constraints, estimated models may contradict biological knowledge and estimation methods may over-fit. RESULTS: In this report, we extended expectation-maximization (EM) algorithms to incorporate prior network structure and to estimate genetic regulatory networks that can track and predict gene expression profiles. We applied our method to synthetic data and to SOS data and showed that our method significantly outperforms the regular EM without structural constraints. AVAILABILITY: The Matlab code is available upon request and the SOS data can be downloaded from http://www.weizmann.ac.il/mcb/UriAlon/Papers/SOSData/, courtesy of Uri Alon. Zak's data is available from his website, http://www.che.udel.edu/systems/people/zak.     

Modular modeling of cellular systems with ProMoT/Diva

MOTIVATION: Need for software to setup and analyze complex mathematical models for cellular systems in a modular way, that also integrates the experimental environment of the cells. RESULTS: A computer framework is described which allows the building of modularly structured models using an abstract, modular and general modeling methodology. With this methodology, reusable modeling entities are introduced which lead to the development of a modeling library within the modeling tool ProMot. The simulation environment Diva is used for numerical analysis and parameter identification of the models. The simulation environment provides a number of tools and algorithms to simulate and analyze complex biochemical networks. The described tools are the first steps towards an integrated computer-based modeling, simulation and visualization environment Availability: Available on request to the authors. The software itself is free for scientific purposes but requires commercial libraries. SUPPLEMENTARY INFORMATION: http://www.mpi-magdeburg.mpg.de/projects/promot     

Reconstructing the regulatory network controlling commitment and sporulation in Physarum polycephalum based on hierarchical Petri Net modelling and simulation

We reconstruct the regulatory network controlling commitment and sporulation of Physarum polycephalum from experimental results using a hierarchical Petri Net-based modelling and simulation framework. The stochastic Petri Net consistently describes the structure and simulates the dynamics of the molecular network as analysed by genetic, biochemical and physiological experiments within a single coherent model. The Petri Net then is extended to simulate time-resolved somatic complementation experiments performed by mixing the cytoplasms of mutants altered in the sporulation response, to systematically explore the network structure and to probe its dynamics. This reverse engineering approach presumably can be employed to explore other molecular or genetic signalling systems where the activity of genes or their products can be experimentally controlled in a time-resolved manner.     

Identification of genetic networks

In this report, we propose the use of structural equations as a tool for identifying and modeling genetic networks and genetic algorithms for searching the most likely genetic networks that best fit the data. After genetic networks are identified, it is fundamental to identify those networks influencing cell phenotypes. To accomplish this task we extend the concept of differential expression of the genes, widely used in gene expression data analysis, to genetic networks. We propose a definition for the differential expression of a genetic network and use the generalized T2 statistic to measure the ability of genetic networks to distinguish different phenotypes. However, describing the differential expression of genetic networks is not enough for understanding biological systems because differences in the expression of genetic networks do not directly reflect regulatory strength between gene activities. Therefore, in this report we also introduce the concept of differentially regulated genetic networks, which has the potential to assess changes of gene regulation in response to perturbation in the environment and may provide new insights into the mechanism of diseases and biological processes. We propose five novel statistics to measure the differences in regulation of genetic networks. To illustrate the concepts and methods for reconstruction of genetic networks and identification of association of genetic networks with function, we applied the proposed models and algorithms to three data sets.     

感受态还是芽胞？细胞命运决定的遗传调控网络

枯草芽胞杆菌作为一般认为安全(GRAS,Generally recognized as safe)菌株,被广泛应用于饲料、食品、生物防治等领域,同时,枯草芽胞杆菌作为表达宿主在工业酶的应用中扮演重要角色。然而,低效的芽胞形成率与感受态效率极大限制了枯草芽胞杆菌的应用潜力。尽管已有大量关于芽胞形成与感受态形成的分子遗传机制的研究报道,但是通过遗传改造提高枯草芽胞杆菌芽胞形成率与感受态效率的研究报道并不多。可能的原因是芽胞形成与感受态形成作为枯草芽胞杆菌生长后期两个主要的发育事件,受胞内复杂的遗传调控机制操纵,且两个遗传通路之间存在相互调控关系,对遗传改造工作形成挑战。随着基因工程与代谢工程研究的不断发展,积累了大量关于细胞生长、代谢与发育等方面的遗传信息,通过综合这些遗传信息构建细胞遗传调控网络,用于指导生产实践,已经成为当前研究的热点之一。基于此,本文简要概述了枯草芽胞杆菌芽胞形成和感受态形成的遗传通路,初步探讨了芽胞形成与感受态形成之间的遗传调控网络,及细胞在生长后期的遗传决定机制,并讨论了该遗传调控网络对枯草芽孢杆菌及其近缘种应用研究的指导作用。